How to create Non-Central Student's T distribution and what priors to use with the distribution?

Questions
4

Thank you for the comment. Well, I am looking online in order to convert the function to theano, the only thing that I found to define the function is from the following GitHub link hyp1f1 function GitHub

Will this be enough to use in order to convert the function into theano? In addition, I have a question, it is okay to use NumPy arrays with theano?

Also, I thought of another way but I am not sure if this can be implemented, I looked into the nct function in scipy and what they wrote the following,

If Y is a standard normal random variable and V is an independent chi-square random variable ( chi2 ) with k degrees of freedom, then

X=(Y+c) / sqrt(V/k)

has a non-central Student’s t distribution on the real line. The degrees of freedom parameter k (denoted df in the implementation) satisfies k>0 and the noncentrality parameter c (denoted nc in the implementation) is a real number.

The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the loc and scale parameters. Specifically, nct.pdf(x, df, nc, loc, scale) is identically equivalent to nct.pdf(y, df, nc) / scale with y = (x - loc) / scale .

So, I thought of only using the priors as normal and chi2 random variables code part in their distributions and use the degree of freedom variable as mentioned before in the code into the equation mentioned in SciPy, will it be enough to get the distribution?